Riemannian Geometry Approach for Minimizing Distortion and its Applications
Abstract
Given an affine transformation T, we define its Fisher distortion DistF(T). We show that the Fisher distortion has Riemannian metric structure and provide an algorithm for finding mean distorting transformation -- namely -- for a given set \Ti\i=1N of affine transformations, find an affine transformation T that minimize the overall distortion Σi=1NDistF2(T-1Ti). The mean distorting transformation can be useful in some fields -- in particular, we apply it for rendering affine panoramas.
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